Question

How do I rewrite sqrt(sqrt(x))?

I answered with this (http://i.imgur.com/UtTFboI.png), and it was correct (on MathXL) but it said I had to rewrite it in the "correct" way.. I have no idea how else to write it.. Help please.

Answer 1

Well you know that the square root is just the opposite of squaring something right? Well if you know that and that exponents multiply each other we can figure out that we can really rewrite a square root as a 1/2 exponent. See: \[(x^{1/2})^2=x^{2*(1/2)}=x^1=x\]

So there is one possibility and that is your answer should look like: \[(x^{1/2})^{1/2}=x^{(1/2)*(1/2)}=x^{1/4}\]

Answer 2

Makes perfect sense, thank you. :)